Simple events

Simple events are events that can only occur exclusively. In other words, they are events that have one outcome. For example, the card selected from a normal deck is a 9 of hearts. This event can only happen in one way.

Another way to understand simple events is through sample points and sample space. A possible outcome in an event is called a sample point. From the previous example, one of the sample points would be 1. All the outcomes of an experiment comprise the sample space. For example, the sample space in the event of rolling a dice would be 1,2,3,4,5,6. So, A simple event is an event with a single sample point in a sample space. For example, Rolling a 2 on a dice is a simple event with a single sample point.

Probability and Simple Events

Probability

Probability is the measurement of the likelihood of an event occurring. If the likelihood is higher, the probability will be higher. If the likelihood is lower, the probability will be lower.

The probability of simple events can be calculated by the formula mentioned below: 

Probability (event) = the number of favourable outcomes/number of possible outcomes

Some important things to keep in mind while calculating probabilities of simples events are:

• Probability can be a fraction, decimal, whole number, or expressed as a percentage. 
• The probability of an impossible event is always 0 as the number of favourable outcomes is 0.
• The probability of a sure event is 1 as all the number of favourable outcomes will be equal to the number of total outcomes.
• In this way, the probability is always between 1 and 0.
• The probabilities of all possible outcomes or all outcomes in the sample place will add up to 1.

The probability line is an excellent way to understand all these concepts. A probability line 

visually depicts the range of probabilities and what they mean. 

Calculating Probability of Simple Events 

Example 1

The probability of getting a 3 on a dice. 

The number of favourable outcomes in this event = 1, as it is a dice, the number of possible outcomes = 6

Since Probability = number of favourable outcomes/ number of possible outcomes.

Probability (event) = ⅙.

Example 2

The probability of pulling a heart face card from a normal deck (excluding jokers).

The number of favourable outcomes = king of hearts, queen of hearts, jack of hearts = 3

Number of total outcomes = 52

Therefore, probability(E) = 3/52 

This event is a combination of 3 simple events.

Theoretical and Experimental Probability

• Classical or theoretical probability model

This model assumes that each event is equally likely to occur. For example, when we say that the probability of rolling a 3 on a dice, is ⅙ we assume that each number landing on top is equally likely. Therefore, this is the classical model of probability.

• Experimental or empirical probability

It is based on historical data. As it is based on historical data, it takes no such assumptions. The formula for experimental probability is similar to the classical model. 

Experimental probability = Times event occurred/Total number of trials.

For example, if a dice is rolled six times and it lands on an even number 4 out 6 times. The times an event occurred is 4 and the total trials are 6.

 Therefore, experimental probability(E) = 4/6 or ⅔. 

According to the classical model, Probability(E) = 3/6 or ½. 

The difference between the two models occurs as the classical model assumes that each outcome is equally likely and gives only a theoretical probability. On the other hand, the experiment takes into account the empirical data and gives us the real probability. 

Simple and Compound Events

A simple event is distinct from a compound event. The easiest way to understand the difference and enhance our understanding of simple events is to go back to the example of cards. Considering that a normal deck of cards has 13 hearts. The event of a card being picked from a deck being a heart is an example of a compound event as it can happen in 13 different ways. We can say it comprises 13 simple events. In this way, we can understand that simple and compound events are not opposites but instead, compound events comprise multiple simple events. 

Examples of simple events in daily life

The best way to grasp core concepts is by analyzing their occurrence in real life. This will allow a person to understand its practical importance and ingrain said concepts into the person’s mind. It also enables us to visualize different problems of probability in terms of these common examples. 

• The event of flipping a coin
• The event of getting number 5 when rolling a dice
• The event of picking a 9 of hearts from a deck of 52 Cards 
• The event of your blood group being 0+.

Conclusion

SImple events are events that have one outcome. They are vital in grasping more complex topics in probability. The probability of simple events can be found by dividing the number of favourable outcomes from all the possible outcomes. The answer after the division will be a number between 1 and 0. The bigger the answer, the higher the likelihood. This method of calculating the probability is the classic model of probability. Probability can also be calculated by the empirical method. The study material notes on simple events make sure you now have a solid base of knowledge to understand compound events, complementary events, etc.